Smelly sneakers need to be cleaned and washed immediately. Otherwise, this will breed bacteria that may trigger the appearance of skin diseases such as athlete's foot. But you do not have to do this manually. If you have a washing machine, you can do it using your washer.
Here is a step-by-step procedure on how to clean your dirty shoes:
Step 1: If it has shoe laces, remove it first. Other shoes are fastened using Velcro and it is okay to wash that using your washing machine. But the shoe laces have to be removed first. You can include this with your other laundry. Once it is cleaned, you can just hang it to dry completely.
Step 2: Mix your cleaning solution. If it is reliably clean, you only need to use a mild soap. However, I suggest you use a disinfecting detergent specifically used for shoes. Before you buy it, check if it is a good choice for the materials of your shoes. If you are using canvas sneaker, make sure the detergent you are using will work well with canvas materials.
Step 3: Apply the solution to the dirtiest areas first. You might also want to sprinkle baking soda if it is extremely smelly. After treating it with the solution, place it in a net bag. You use this for exclusive clothes but you can also use this to hold shoes together.
Step 4: Set washing machine to the hot water cycle. And use the gentle washing cycle. Add a bit more of the solution to the washing cycle and allow the machine to finish cleaning your shoes.
Step 5: Use the slow spin speed so it can tumble and extract some of the excess water. When the cycle is done, hang it in a warm and sunny place to dry completely.
You might want to clean your washer afterwards as the dirt from your sneakers will be left on the washing machine's drum. If you do not immediately clean it off, it might cause a smelly washer and you do not want that to happen.
Using baking soda is also a good choice for a cleaning solution if you do not have a detergent used for athletic shoes ready. Just sprinkle it before washing your shoes. If it is still smelly after drying it completely, sprinkle it again with baking soda for an effective way of diffusing the smell.